Equality Measures in Discrete Location Models

In the last decades, a new class of location problems has been defined aiming at balancing distances among users and facilities. The balancing objectives are related to the achievement of an “equity” goal which is linked, in turn, to the concept of “equality”. Erkut (1993), and Marsh and Schilling (1994) proposed lists of equity measures and also introduced a framework for their classification. Another very comprehensive survey on the topic was performed by Eiselt and Laporte (1995).

In literature we can observe two main different lines of research regarding location models with equity objectives. A first line concerns the formulation of versions of location problems involving equity measures with the proposal of efficient algorithms for solving them (see for instance Drezner and Drezner (2007), Marin et al. (2010)). A second line of research deals with the analysis of properties that equality measures should satisfy (see for instance Drezner et al.( 2009)).

Given the quite large number of equity measures that have been introduced, there is a concern about their intrinsic meaning and ability in keeping track of equity issues. We propose an analysis of an extensive list of equality measures in order to individuate potential correlations between pairs of measures and to define new properties useful to design appropriate procedures to solve location models with equaliity objectives.

The results of the performed analysis represent the basis to provide comments about similarity among the measures, common behaviors of subsets of measures, and to individuate “more representative” measures.